Find (f∘g)(x).
f(x)=x+4
g(x)=x2+5x
Write your answer as a polynomial in simplest form.
(f∘g)(x)=
(f∘g)(x) would be equal to f(g(x)). Therefore, we need to substitute g(x) into f(x).
f(g(x)) = f(x^2 + 5x)
Now substitute x^2 + 5x into f(x):
f(x^2 + 5x) = (x^2 + 5x) + 4
Simplifying, the final polynomial form is:
(f∘g)(x) = x^2 + 5x + 4
To find (f∘g)(x), we need to substitute g(x) into f(x):
(f∘g)(x) = f(g(x))
g(x) = x^2 + 5x
Now substitute g(x) into f(x):
f(g(x)) = f(x^2 + 5x)
f(x) = x + 4
Distribute f(x) to each term in g(x):
f(x^2 + 5x) = (x^2 + 5x) + 4
Simplify the polynomial:
(f∘g)(x) = x^2 + 5x + 4
To find (f∘g)(x), we need to substitute the function g(x) into the function f(x).
Let's start by determining g(x) first.
g(x) = x^2 + 5x
Now, substitute g(x) into f(x) using the function composition notation (f∘g)(x):
(f∘g)(x) = f(g(x))
Substituting g(x) into f(x):
(f∘g)(x) = f(g(x)) = (x^2 + 5x) + 4
Now, simplify the polynomial by adding like terms:
(f∘g)(x) = x^2 + 5x + 4
Therefore, (f∘g)(x) = x^2 + 5x + 4.